An iterative method for solving the generalized total least squares problem

This paper introduces a novel method for solving the generalized total least squares problem, an extension of the total least squares problem. The generalized total least squares problem emerges when solving overdetermined linear systems with the multiple right-hand sides \mathbf{AX} \thickapprox \mathbf{B}, where both the observation matrix \mathbf{B} and the data matrix \mathbf{A} contain errors. Our approach involves extending the Taylor series expansion to reformulate the generalized total least squares problem into a linear problem, allowing us to employ the tensor form of the generalized least squares algorithm for efficient computation. This technique streamlines the computational process and enhances solution accuracy. For a more detailed survey, we compare the proposed method for solving the generalized total least squares problem with one of the matrix format methods for the associated total least squares problem. Empirical results show that our method significantly improves computational efficiency and solution precision. Additionally, we demonstrate its practical application in the context of image blurring.

کلیدواژه ها:

Least squares problem ، total least squares problem ، tensor form of the generalized least squares problem ، Taylor series expansion ، Image deblurring